Notes on quantization of symplectic vector spaces over finite fields
نویسندگان
چکیده
In these notes we construct a quantization functor, associating an Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main technical result is a proof of a stronger form of the Stone-von Neumann theorem for the Heisenberg group over Fq. Our result answers, for the case of the Heisenberg group, a question of Kazhdan about the possible existence of a canonical Hilbert space attached to a coadjoint orbit of a general unipotent group over Fq.
منابع مشابه
Notes on Canonical Quantization of Symplectic Vector Spaces over Finite Fields
In these notes we construct a quantization functor, associating a Hilbert space H(V ) to a finite dimensional symplectic vector space V over a finite field Fq. As a result, we obtain a canonical model for the Weil representation of the symplectic group Sp (V ). The main technical result is a proof of a stronger form of the Stonevon Neumann theorem for the Heisenberg group over Fq. Our result an...
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